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The following justifies the follower range we take.

Now comes the 3 maps.

Here comes the regression. METRO_ID Patents GDP Population Greenspace Employment 1 Aachen 3.76 28089.46 581472 246.60 0.69 2 Akron 2.09 35580.47 542004 1285.57 0.18 3 Albany 2.00 37696.66 829004 1932.18 0.27 4 Albuquerque 0.73 38059.97 852670 71.24 0.27 5 Amsterdam 1.18 40064.41 2317340 219.26 14.13 6 Antwerp 1.08 38605.43 1040008 318.68 10.29 7 Atlanta 1.27 42352.45 4202262 111.10 1.42 8 Augsburg 2.10 33635.88 594054 751.96 0.78 9 Austin 2.68 48858.72 1608564 172.01 0.51 10 Baltimore 1.32 61804.14 1939607 1000.03 0.68 11 Barcelona 0.93 33874.36 3594393 2.45 8.69 12 Berlin 1.76 29518.57 4363940 207.68 5.20 13 Bilbao 0.39 34422.73 989856 212.52 2.26 14 Bochum 1.12 30195.18 658177 27.07 0.78 15 Bologna 1.55 38091.72 736403 190.64 1.47 16 Bonn 2.07 38812.14 743893 116.29 0.88 17 Bordeaux 0.89 29560.46 1096729 1349.14 1.75 18 Boston 6.10 50324.49 3616814 87.66 1.24 19 Bremen 0.88 38125.37 1024841 1424.72 1.01 20 Brussels 1.24 45709.90 2436174 303.11 21.78 21 Buffalo 1.21 33529.23 1142342 2311.87 0.37 22 Catania 0.23 18246.96 620503 35.63 0.79 23 Charleston 0.62 39554.74 639308 473.77 0.20 24 Charlotte 1.02 39155.43 1219694 836.32 0.39 25 Chicago 1.71 48556.19 9231469 430.16 3.11 26 Cincinnati 2.47 40922.34 2065761 3045.68 0.68 27 Cleveland 2.04 37605.18 1531657 501.03 0.51 28 Cologne 2.04 39323.97 1892004 71.59 2.24 29 Columbia 0.41 33109.26 623161 220.80 0.19 30 Columbus 1.15 37760.92 1661412 1917.88 0.56 31 Copenhagen 3.72 37476.61 1972725 386.18 36.85 32 Dallas 1.40 48973.56 3966038 225.75 1.26 33 Dayton 0.84 34588.17 698590 1111.72 0.23 34 Denver 1.31 51317.29 2418085 5.24 0.89 35 Detroit 1.49 37162.84 3897193 538.08 1.23 36 Dortmund 1.16 30762.06 832638 63.68 0.98 37 Dresden 2.31 26196.74 832097 517.75 1.00 38 Duisburg 1.09 35080.35 819201 123.94 0.97 39 Dusseldorf 3.02 42111.38 1428489 53.80 1.69 40 Essen 1.19 32557.03 765005 40.97 0.90 41 Florence 0.81 35318.30 718528 510.26 1.34 42 Frankfurt 2.89 50127.40 2510347 101.07 3.11 43 Freiburg 2.77 33543.46 523171 595.76 0.69 44 Fresno 0.20 31447.09 1047811 83.58 0.34 46 Genova 0.63 31162.97 720659 330.63 1.28 47 Ghent 1.61 29813.10 568747 754.47 5.63 48 Gothenburg 4.31 32772.08 866669 302.92 9.56 49 Graz 2.61 35643.12 596616 924.67 7.11 50 Grenoble 5.58 30797.70 642731 1115.82 1.05 51 Hague 1.68 36914.72 856025 21.82 5.22 52 Hamburg 1.76 46054.42 2973464 925.06 3.78 53 Hanover 2.01 36179.87 1225512 559.11 1.52 54 Harrisburg 0.67 36048.71 565403 3864.52 0.19 55 Helsinki 3.48 44733.98 1435086 80.77 31.11 56 Hiroshima 1.44 29829.75 1395689 11.69 1.06 57 Houston 2.96 53641.37 5363803 719.04 1.70 58 Indianapolis 1.74 38088.56 1607756 1064.91 0.53 60 Jacksonville 0.47 41632.01 1122012 193.80 0.37 61 Karlsruhe 3.04 41520.09 682950 224.10 0.90 64 Leipzig 0.74 25773.74 841674 361.39 1.02 65 Liege 0.52 25117.72 719881 496.48 6.16 66 Lille 0.64 26099.21 1342383 41.26 1.93 67 Linz 2.04 39714.94 601505 1735.10 7.47 68 Lisbon 0.14 31508.02 2758968 66.52 25.55 69 Louisville 0.70 37792.79 1201653 4304.60 0.37 70 Lyon 2.81 37866.19 1863301 496.18 3.04 71 Madison 3.06 39182.80 531023 5081.25 0.19 72 Madrid 0.62 37185.59 6259099 27.40 15.49 74 Malmo 6.86 30325.86 647057 881.78 6.97 75 Mannheim 5.28 36923.54 1246471 83.01 1.59 76 Marseille 1.22 30386.16 1697613 48.68 2.60 77 Memphis 1.05 35697.94 1253006 3239.39 0.39 78 Miami 0.64 41419.94 5448094 150.16 1.78 79 Milwaukee 1.22 42417.81 1544538 1602.99 0.56 80 Minneapolis 5.21 45685.38 3212176 3061.19 1.16 82 Monterrey 0.07 25972.52 3915469 51.31 3.97 83 Montpellier 1.27 27291.98 618454 208.60 0.88 84 Munich 4.94 51791.38 2786626 574.58 3.66 85 Nagoya 1.65 33972.34 6364462 7.62 5.25 86 Nantes 0.67 30722.43 851118 605.80 1.37 87 Naples 0.17 17664.71 3544063 13.02 4.43 88 Nashville 0.62 39029.00 1198031 4474.39 0.38 89 Nice 2.06 30787.97 835633 234.02 1.28 91 Okayama 1.27 23797.03 875734 85.30 0.67 92 Omaha 0.34 45122.77 844399 756.54 0.31 93 Orlando 0.75 33993.40 1747437 566.42 0.57 94 Osaka 2.59 31069.86 17211139 10.99 12.84 95 Oslo 1.99 46010.78 1189595 316.50 26.18 96 Palermo 0.12 18962.79 934310 44.80 1.18 97 Palmas 0.07 25158.10 647252 84.90 1.41 98 Paris 2.14 49956.64 11529670 92.85 20.33 99 Philadelphia 1.78 49099.64 4004502 378.71 1.33 100 Phoenix 1.03 42304.44 3654911 10.51 1.22 101 Pittsburgh 1.87 40246.89 1234856 610.85 0.41 102 Portland 2.00 44955.78 2162610 445.87 0.74 103 Porto 0.22 21552.00 1294369 67.33 12.25 104 Providence 0.90 51413.36 842024 123.13 0.29 105 Raleigh 3.88 38566.27 1054223 1758.04 0.33 106 Rennes 2.34 29317.47 652633 520.34 1.04 107 Richmond 0.37 42274.02 500350 214.51 0.18 108 Rome 0.52 37664.43 3941844 236.61 7.03 109 Rotterdam 1.07 38438.17 1473917 72.38 8.99 110 Rouen 0.68 27225.02 691978 677.19 1.08 111 Seattle 4.36 53267.17 2581101 106.62 0.89 112 Seville 0.29 22549.37 1384844 14.26 2.68 113 Stockholm 5.68 47443.31 1938753 119.36 22.89 114 Strasbourg 1.40 30999.50 750126 365.43 1.34 115 Stuttgart 6.28 44090.18 1949365 177.84 2.58 117 Tallinn 0.41 28456.85 530889 1468.15 39.39 118 Tampa 0.65 38472.95 1179272 481.46 0.39 119 Tokyo 2.53 38165.44 34482742 4.75 27.95 120 Toledo 1.31 35954.40 444432 569.45 0.15 122 Toulouse 2.80 33391.99 1175096 185.78 1.98 123 Tucson 1.70 35108.24 951298 1.13 0.32 124 Tulsa 0.68 40129.72 931604 2200.96 0.29 125 Turin 1.07 32193.76 1734766 244.26 3.24 126 Utrecht 1.61 42593.86 698897 240.49 4.26 127 Valencia 0.56 27582.47 1525303 15.62 3.55 128 Venice 0.49 34748.66 540352 1.19 1.05 129 Vienna 1.32 41262.05 2630118 235.79 30.76 130 Washington 1.39 57145.96 5098743 1150.43 1.79 131 Wichita 0.58 35942.60 577946 42.34 0.20 132 Zaragoza 0.77 31437.99 802680 58.03 1.87 Pollution lon lat Followers 1 10 1 18.50 6.0838868 50.775346 3.42234880 2.85482362 0.275163722 2 16.35 -81.5190053 41.081445 0.95940251 0.73800193 0.129150338 3 11.23 -73.7562317 42.652579 1.44752016 1.26658014 0.072376008 4 8.55 -106.6099910 35.110703 1.71226852 1.44252759 0.093822933 5 22.57 4.8951679 52.370216 6.70164930 5.32938628 0.608456247 6 23.02 4.4024643 51.219448 1.46152722 1.24999038 0.115383728 7 16.20 -84.3879824 33.748995 4.22153593 3.60044186 0.326014894 8 20.83 10.8977900 48.370545 1.19517754 0.89217479 0.151501379 9 9.67 -97.7430608 30.267153 17.66793239 14.33576780 1.566614695 10 20.65 -76.6121893 39.290385 2.88718282 2.29427920 0.283562598 11 14.88 2.1734035 41.385064 4.44581324 3.63343686 0.447919857 12 20.32 13.4049540 52.520007 9.80306787 7.43135790 1.095340449 13 10.61 -2.9349852 43.263013 1.05065787 0.79809588 0.191947111 14 23.78 7.2162363 51.481845 0.62293274 0.53177185 0.030386963 15 24.10 11.3426163 44.494887 1.90113294 1.71101965 0.135795210 16 20.14 7.0982068 50.737430 2.75577267 2.39281725 0.255413077 17 13.40 -0.5791800 44.837789 2.83570508 2.48922022 0.164124410 18 11.51 -71.0597732 42.358431 8.01534168 6.53890413 0.727159318 19 18.05 8.8016937 53.079296 2.02958313 1.74661240 0.185394612 20 23.13 4.3517103 50.850340 1.52698453 1.29711589 0.147772696 21 16.93 -78.8783689 42.886447 2.13596279 1.83832863 0.166324971 22 12.86 15.0830304 37.507877 0.53182660 0.49959468 0.016115958 23 10.89 -79.9310512 32.776475 3.61328186 2.78426048 0.516183123 24 15.14 -80.8431267 35.227087 3.16472820 2.64000643 0.286957220 25 16.37 -87.6297982 41.878114 3.83687580 3.02877039 0.432217234 26 15.71 -84.5120196 39.103118 1.98474073 1.61199674 0.212996566 27 19.44 -81.6943605 41.499320 2.00436521 1.64527698 0.195866307 28 22.41 6.9602786 50.937531 2.56870493 2.05073562 0.232557648 29 12.82 -74.2973330 4.570868 6.80402015 5.72885659 0.561652607 30 19.68 -82.9987942 39.961176 3.24422840 2.70853948 0.282891902 31 15.95 12.5683371 55.676097 4.76498245 3.99447465 0.375115640 32 14.45 -96.8004511 32.780140 2.50375816 2.12806836 0.176498561 33 17.87 -84.1916069 39.758948 1.46008388 1.25968021 0.114516383 34 8.88 -104.9847179 39.737567 5.22727696 4.11482640 0.578970549 35 17.09 -83.0457538 42.331427 0.76978482 0.64918520 0.061582785 36 22.74 7.4652981 51.513587 1.30909231 1.15296203 0.084070148 37 18.25 13.7372621 51.050409 3.73754502 3.11261788 0.420624038 38 25.42 6.7623293 51.434408 0.32958944 0.28076138 0.012207016 39 24.09 6.7734556 51.227741 0.04900283 0.03500202 0.000000000 40 23.56 7.0115552 51.455643 0.75816498 0.61437507 0.052287240 41 11.27 11.2480006 43.771033 1.18297408 0.97421395 0.083504053 42 19.21 8.6821267 50.110922 1.22293850 1.04766393 0.075686748 43 17.57 7.8421043 47.999008 2.38927616 2.06433461 0.172027884 44 14.62 -119.7725868 36.746842 0.69669053 0.56307865 0.066805941 46 14.83 8.9462560 44.405650 0.43016184 0.37465708 0.041628565 47 23.88 3.7174243 51.054342 2.49671647 1.95165865 0.351650207 48 10.01 11.9745600 57.708870 4.03845067 3.42691385 0.426921928 49 16.14 15.4395040 47.070714 2.41361278 2.14543358 0.134089599 50 11.58 5.7245240 45.188529 4.40308621 3.96744517 0.248937736 51 21.87 4.3006999 52.070498 1.17987208 0.95791595 0.070091411 52 17.71 9.9936818 53.551085 4.39554674 3.58504424 0.410295870 53 18.96 9.7320104 52.375892 0.52223071 0.44879202 0.040799274 54 16.16 -76.8867008 40.273191 0.56596799 0.47753549 0.017686500 55 8.55 24.9410248 60.173324 4.85685178 3.95098273 0.550489657 56 12.93 132.4552927 34.385203 0.28659680 0.22211252 0.014329840 57 10.96 -95.3693896 29.760193 1.32555204 1.11674497 0.109996583 58 18.65 -86.1580680 39.768403 2.57501760 2.15206785 0.236354273 60 11.06 -81.6556510 30.332184 1.32797154 1.10515752 0.106950728 61 19.97 8.4036527 49.006890 5.38838861 4.12914562 0.629621495 64 22.00 12.3730747 51.339695 3.17224959 2.50690885 0.368313623 65 20.25 5.5796662 50.632557 0.15280303 0.13891185 0.000000000 66 26.45 3.0572560 50.629250 2.57750582 2.17523613 0.223483164 67 19.31 14.2858300 48.306940 1.41312209 1.13049767 0.083124829 68 12.74 -9.1393366 38.722252 1.79052457 1.49693654 0.166729009 69 15.17 -85.7584557 38.252665 1.88074261 1.63108651 0.133149919 70 18.19 4.8356590 45.764043 3.67090449 2.95175068 0.354210082 71 10.87 -89.4012302 43.073052 11.22361932 9.35929329 0.828589345 72 14.49 -3.7037902 40.416775 2.65213891 2.15685996 0.255627847 74 14.20 13.0038220 55.604981 0.10818212 0.09272753 0.000000000 75 21.94 8.4660395 49.487459 0.68994786 0.59367607 0.048135897 76 12.42 5.3697800 43.296482 0.83646862 0.74221863 0.035343744 77 14.00 -90.0489801 35.149534 0.96567774 0.83000401 0.055865654 78 12.41 -80.2040435 25.789097 0.87370005 0.74521475 0.067913659 79 14.22 -87.9064736 43.038902 1.80636540 1.51501614 0.174809555 80 12.20 -93.2666700 44.983334 2.83608370 2.33797899 0.261504974 82 14.25 -100.3161126 25.686614 0.38309587 0.34223231 0.017877807 83 12.41 3.8767160 43.610769 3.84830561 3.37939443 0.210201567 84 21.07 11.5819806 48.135125 4.28475152 3.57062627 0.362445481 85 24.79 136.9063980 35.181446 0.16497860 0.13198288 0.007856124 86 13.97 -1.5536210 47.218371 4.73494862 3.94774873 0.493468591 87 15.17 -81.7948103 26.142036 0.12697291 0.11568643 0.002821620 88 14.40 -86.7833330 36.166667 5.26697556 3.94814491 0.600986118 89 15.06 7.2619532 43.710173 1.10096179 1.01719295 0.035900928 91 19.25 133.9195019 34.655146 0.26263683 0.15986590 0.079932948 92 12.00 -95.9979883 41.252363 4.19233088 3.75414940 0.236854852 93 10.78 -81.3792365 28.538335 3.22186150 2.74688015 0.257520014 94 21.16 135.5021651 34.693738 0.19173629 0.14757884 0.023240763 95 6.50 10.7522454 59.913869 10.23037252 8.22128540 1.126433786 96 10.85 13.3612671 38.115688 0.36390491 0.29968640 0.042812343 97 7.99 -48.3242858 -10.249091 1.46774363 1.26689450 0.123599464 98 18.28 2.3522219 48.856614 4.08684724 3.32967032 0.376420140 99 20.51 -75.1637890 39.952335 2.95417508 2.39230746 0.252216131 100 9.10 -112.0740373 33.448377 1.07800163 0.89195058 0.087553432 101 17.65 -79.9958864 40.440625 9.01319668 7.52314440 0.785516692 102 5.85 -122.6762071 45.523452 11.30578329 8.30015583 1.202250984 103 15.78 -8.6291053 41.157944 6.31195586 5.07583232 0.664416407 104 11.09 -71.4128343 41.823989 2.54149525 2.05457327 0.320655943 105 13.83 -78.6381787 35.779590 5.61551019 4.72385823 0.559653887 106 15.59 -1.6777926 48.117266 3.24838002 2.83467125 0.229838209 107 15.37 -77.4360481 37.540725 5.95583092 4.83661437 0.459678225 108 13.59 12.4801802 41.872389 0.95133141 0.80419215 0.071032745 109 24.06 4.4777325 51.924420 1.95397706 1.72329921 0.142477494 110 16.73 1.0999710 49.443232 0.70811500 0.62140704 0.028902653 111 6.02 -122.3320708 47.606209 17.31044233 14.03664560 1.561349207 112 14.16 -5.9844589 37.389092 0.64267167 0.49103004 0.064989270 113 7.80 18.0685808 59.329324 10.56864902 8.46936149 1.016117061 114 21.84 7.7478820 48.583148 2.54623890 2.10631281 0.306615155 115 19.16 9.1817588 48.775418 1.91857348 1.65694983 0.123117015 117 7.20 24.7535746 59.436961 3.76726585 3.29635762 0.301381268 118 12.18 -82.4571776 27.950575 2.39978563 2.08603274 0.169596158 119 22.35 139.6917064 35.689487 1.33284064 0.99934048 0.144710070 120 17.31 -83.5552120 41.663938 1.30503654 1.21503402 0.067501890 122 12.89 1.4442090 43.604652 3.53162635 2.96997011 0.399967322 123 7.45 -110.9264790 32.221743 1.95522328 1.77652008 0.084095625 124 10.49 -95.9927750 36.153982 2.10389822 1.81407551 0.128810095 125 29.89 7.6868565 45.070312 0.65138468 0.56491769 0.046115730 126 19.85 5.1177780 52.091667 4.52141016 3.82030542 0.443556060 127 14.04 -0.3762881 39.469907 1.98649055 1.75702795 0.144233638 128 31.44 12.3155151 45.440847 2.31330688 1.86915196 0.240583916 129 20.84 16.3738189 48.208174 3.74127701 3.03408440 0.311773084 130 18.74 -77.0368707 38.907192 4.31086642 3.44006356 0.427556360 131 10.21 -97.3361110 37.688889 2.11092386 1.93789731 0.086513273 132 19.81 -0.8890853 41.648823 1.32057607 1.10878557 0.062291324 20 30 40 50 60 1 0.120384129 0.017197733 0.017197733 0.034395465 0.034395465 2 0.036900097 0.000000000 0.018450048 0.018450048 0.000000000 3 0.060313340 0.024125336 0.000000000 0.000000000 0.012062668 4 0.058639333 0.023455733 0.023455733 0.011727867 0.011727867 5 0.289124600 0.129458776 0.073359973 0.038837633 0.038837633 6 0.038461243 0.009615311 0.019230621 0.000000000 0.000000000 7 0.099946172 0.071390123 0.035695061 0.016657695 0.014278025 8 0.067333946 0.033666973 0.000000000 0.050500460 0.000000000 9 0.609239048 0.273535899 0.236235549 0.118117775 0.111901050 10 0.061868203 0.077335254 0.046401152 0.025778418 0.015467051 11 0.155798211 0.069552773 0.047295886 0.016692665 0.019474776 12 0.437677878 0.245191272 0.146656462 0.107700839 0.054996173 13 0.020204959 0.010102480 0.010102480 0.000000000 0.000000000 14 0.000000000 0.000000000 0.045580444 0.000000000 0.000000000 15 0.013579521 0.040738563 0.000000000 0.000000000 0.000000000 16 0.040328381 0.013442794 0.040328381 0.013442794 0.000000000 17 0.072944182 0.036472091 0.018236046 0.036472091 0.000000000 18 0.235013468 0.160362131 0.094005387 0.052532422 0.027648643 19 0.048788056 0.019515222 0.009757611 0.000000000 0.000000000 20 0.032838377 0.016419188 0.008209594 0.008209594 0.004104797 21 0.035015783 0.035015783 0.000000000 0.008753946 0.017507892 22 0.000000000 0.016115958 0.000000000 0.000000000 0.000000000 23 0.109493390 0.046925738 0.015641913 0.015641913 0.031283826 24 0.073789000 0.040993889 0.032795111 0.008198778 0.008198778 25 0.140822658 0.090993102 0.030331034 0.021665024 0.007582758 26 0.058089973 0.038726648 0.009681662 0.009681662 0.009681662 27 0.058759892 0.032644384 0.000000000 0.000000000 0.006528877 28 0.100422621 0.052854011 0.042283209 0.021141604 0.021141604 29 0.208613825 0.048141652 0.016047217 0.032094435 0.048141652 30 0.132417486 0.030094883 0.018056930 0.006018977 0.018056930 31 0.147004778 0.076036954 0.045622172 0.020276521 0.015207391 32 0.073120832 0.027735488 0.035299712 0.012607040 0.002521408 33 0.028629096 0.028629096 0.014314548 0.014314548 0.000000000 34 0.227452716 0.086845582 0.033084031 0.020677520 0.016542016 35 0.028225443 0.010263798 0.010263798 0.002565949 0.000000000 36 0.060050106 0.000000000 0.012010021 0.000000000 0.000000000 37 0.096142637 0.036053489 0.012017830 0.000000000 0.024035659 38 0.012207016 0.000000000 0.024414033 0.000000000 0.000000000 39 0.014000808 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Regression Estimates of Patent Activity
Dependent variable:
log(Patents)
(1) (2)
(Intercept) 0.25*** (0.07) 0.08 (0.08)
20 Followers
1.90*** (0.40)
GDP -0.11 (0.11)
Population 0.05 (0.05)
Greenspace 0.11* (0.06)
Employment 0.45** (0.21)
Pollution 0.68*** (0.16) -19.58*** (3.82)
Observations 123 123
R2 0.09 0.31
Adjusted R2 0.08 0.27
Residual Std. Error 0.87 (df = 121) 0.78 (df = 116)
F Statistic 12.30*** (df = 1; 121) 8.61*** (df = 6; 116)
Note: p<0.1; p<0.05; p<0.01